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Fundamental characteristics of queues with fluctuating load

Published:26 June 2006Publication History

ABSTRACT

Systems whose arrival or service rates fluctuate over time are very common, but are still not well understood analytically. Stationary formulas are poor predictors of systems with fluctuating load. When the arrival and service processes fluctuate in a Markovian manner, computational methods, such as Matrix-analytic and spectral analysis, have been instrumental in the numerical evaluation of quantities like mean response time. However, such computational tools provide only limited insight into the functional behavior of the system with respect to its primitive input parameters: the arrival rates, service rates, and rate of fluctuation.For example, the shape of the function that maps rate of fluctuation to mean response time is not well understood, even for an M/M/1 system. Is this function increasing, decreasing, monotonic? How is its shape affected by the primitive input parameters? Is there a simple closed-form approximation for the shape of this curve? Turning to user experience: How is the performance experienced by a user arriving into a "high load" period different from that of a user arriving into a "low load" period, or simply a random user. Are there stochastic relations between these? In this paper, we provide the first answers to these fundamental questions.

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      • Published in

        cover image ACM Conferences
        SIGMETRICS '06/Performance '06: Proceedings of the joint international conference on Measurement and modeling of computer systems
        June 2006
        404 pages
        ISBN:1595933190
        DOI:10.1145/1140277
        • cover image ACM SIGMETRICS Performance Evaluation Review
          ACM SIGMETRICS Performance Evaluation Review  Volume 34, Issue 1
          Performance evaluation review
          June 2006
          388 pages
          ISSN:0163-5999
          DOI:10.1145/1140103
          Issue’s Table of Contents

        Copyright © 2006 ACM

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        • Published: 26 June 2006

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